Lecture 18: Ordinary Differential Equations: Second Order
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چکیده
2. General Remarks Second order ODEs are much harder to solve than first order ODEs. First of all, a second order linear ODE has two linearly independent solutions and a general solution is a linear combination of these two solutions. In addition, many popular second order ODEs have singular points. Except for a few cases, the solutions have no simple mathematical expression. However, there is a systematic way to find solutions in a form of series (Frobenius method). Although simple mathematical expressions are not available, the properties of solutions to popular second ODEs are well investigated and the solutions are often known as special functions such as Bessel functions.
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